# Research

##### Working papers

## A New Approach to Self-Normalization

With Yongmiao Hong

Abstract: This paper proposes the range-based estimator to avoid long-run variance estimation in hypothesis testing about the population mean of a time series process. The denominator of the range-based estimator is the so-called adjusted range normalizer which makes use of the well-established properties for adjusted range analysis in measuring long range dependence. Compared to current hypothesis testing approach, the range-based estimator can get rid of choosing tuning parameter or kernel function. In the meantime, the range-based estimator has salient property in the way that it takes into account of the extreme value property in time series data especially under heavy tail distributions. The concrete probability density function form and critical values for the asymptotic distribution for the range-based estimator can be derived explicitly. We perform asymptotic local power comparisons for the range-based estimator and related tests which shows that the range-based estimator has remarkable asymptotic local power performance against a broad class of asymptotic local alternatives. Simulation results reveal incorporating MBB can generally improve the size performance of the range-based estimator in testing the process where the size performance of the range-based estimator is deviate much from the true significance level. Real data analysis for S & P 500 percentage returns series and macroeconomic series also indicates the range-based estimator has outstanding power performance especially when data depicts larger volatility and more observations are available.

## A General Liquidity Risk Model

With Robert Jarrow

Abstract: This paper derives a general liquidity risk model. The paper extends Prof. Jarrow's Asset Market Equilibrium with Liquidity Risk and make the liquidity risk model more complicated. Here we construct a general liquidity risk model includes both convex liquidity risk part and non-convex liquidity risk part. Convex liquidity risk part is modeled as liquidity adjusted amount for stock purchasing times stock price. Non-convex liquidity risk part is modeled as a part of fix liquidity cost minus a part vary with convex liquidity risk part. Then, market's aggregate wealth process can be influenced by such more general liquidity risk process. We define a process g to capture the sum of above two aspects that influence market's aggregate wealth process. Using representative agent approach, an equilibrium asset price is well established and risk return relationship can be characterized using state price density. Several implications are provided accordingly.